I am going through the examples in "Nonlinear Dynamics and Chaos 2ed" (Strogatz 2015) and I don't understand the simplification step for the solution to example 3.2.1. Why is it that the resulting first order system is
\begin{equation} \dot{x} = x -\ ... \end{equation}
instead of
\begin{equation} \dot{x} = x(1 - x^2) -\ ... \end{equation} after the and so? I understand the Taylor expansion, but the simplification of $x(1-x^2)$ to $x$ isn't clear to me. My thought is that because $x$ is close to zero, one might simply ignore the $(1-x^2)$ term in $x(1-x^2)$, but then again, if that is possible, why not just ignore the whole term and say that $x(1-x^2) \approx 0$?
